TSTP Solution File: NUM925_2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:53:08 EDT 2023
% Result : Theorem 14.93s 4.72s
% Output : CNFRefutation 14.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 98
% Syntax : Number of formulae : 125 ( 36 unt; 86 typ; 0 def)
% Number of atoms : 43 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 2 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 82 ( 49 >; 33 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 70 ( 70 usr; 22 con; 0-3 aty)
% Number of variables : 24 (; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
%$ hBOOL > times_times_int > if_nat > hAPP_real_real > hAPP_real_bool > hAPP_r1134773055l_bool > hAPP_nat_real > hAPP_nat_nat > hAPP_nat_int > hAPP_nat_bool > hAPP_n1699378549t_bool > hAPP_int_int > hAPP_int_bool > hAPP_i1948725293t_bool > #nlpp > succ > sqrt > power_power_real > power_power_nat > power_power_int > plus_plus_real > plus_plus_nat > plus_plus_int > number_number_of_nat > number_number_of_int > number267125858f_real > bit1 > bit0 > zero_zero_real > zero_zero_nat > zero_zero_int > tn > t > semiri984289939at_nat > semiri1621563631at_int > semiri132038758t_real > pls > ord_less_real > ord_less_nat > ord_less_int > ord_less_eq_real > ord_less_eq_nat > ord_less_eq_int > one_one_real > one_one_nat > one_one_int > n > m1 > fTrue > fFalse > #skF_16 > #skF_21 > #skF_22 > #skF_9 > #skF_18 > #skF_5 > #skF_13 > #skF_19 > #skF_1 > #skF_4 > #skF_8 > #skF_7 > #skF_15 > #skF_20 > #skF_6 > #skF_14 > #skF_11 > #skF_12 > #skF_2 > #skF_17 > #skF_10 > #skF_3
%Foreground sorts:
tff(fun_int_bool,type,
fun_int_bool: $tType ).
tff(fun_int_fun_int_bool,type,
fun_int_fun_int_bool: $tType ).
tff(real,type,
real: $tType ).
tff(fun_re413263731l_bool,type,
fun_re413263731l_bool: $tType ).
tff(fun_real_real,type,
fun_real_real: $tType ).
tff(fun_nat_bool,type,
fun_nat_bool: $tType ).
tff(fun_int_int,type,
fun_int_int: $tType ).
tff(nat,type,
nat: $tType ).
tff(fun_nat_fun_nat_bool,type,
fun_nat_fun_nat_bool: $tType ).
tff(bool,type,
bool: $tType ).
tff(fun_real_bool,type,
fun_real_bool: $tType ).
tff(int,type,
int: $tType ).
tff(fun_nat_nat,type,
fun_nat_nat: $tType ).
tff(fun_nat_int,type,
fun_nat_int: $tType ).
tff(fun_nat_real,type,
fun_nat_real: $tType ).
%Background operators:
%Foreground operators:
tff(ord_less_eq_real,type,
ord_less_eq_real: fun_re413263731l_bool ).
tff(bit1,type,
bit1: int > int ).
tff('#skF_16',type,
'#skF_16': ( nat * nat * fun_nat_nat ) > nat ).
tff(hAPP_nat_real,type,
hAPP_nat_real: ( fun_nat_real * nat ) > real ).
tff(n,type,
n: nat ).
tff(one_one_int,type,
one_one_int: int ).
tff(semiri132038758t_real,type,
semiri132038758t_real: fun_nat_real ).
tff(fTrue,type,
fTrue: bool ).
tff('#skF_21',type,
'#skF_21': ( nat * nat * fun_nat_nat ) > nat ).
tff(hAPP_int_bool,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(semiri1621563631at_int,type,
semiri1621563631at_int: fun_nat_int ).
tff(number267125858f_real,type,
number267125858f_real: int > real ).
tff(plus_plus_real,type,
plus_plus_real: real > fun_real_real ).
tff(one_one_real,type,
one_one_real: real ).
tff('#skF_22',type,
'#skF_22': ( real * real ) > real ).
tff('#skF_9',type,
'#skF_9': fun_int_bool > int ).
tff(succ,type,
succ: int > int ).
tff(if_nat,type,
if_nat: ( bool * nat ) > fun_nat_nat ).
tff(hAPP_real_real,type,
hAPP_real_real: ( fun_real_real * real ) > real ).
tff(ord_less_int,type,
ord_less_int: fun_int_fun_int_bool ).
tff(power_power_real,type,
power_power_real: real > fun_nat_real ).
tff('#skF_18',type,
'#skF_18': ( fun_int_bool * int * int ) > int ).
tff(zero_zero_real,type,
zero_zero_real: real ).
tff(semiri984289939at_nat,type,
semiri984289939at_nat: fun_nat_nat ).
tff('#skF_5',type,
'#skF_5': ( real * nat ) > real ).
tff('#skF_13',type,
'#skF_13': ( nat * nat ) > nat ).
tff(number_number_of_int,type,
number_number_of_int: int > int ).
tff(hAPP_n1699378549t_bool,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(ord_less_real,type,
ord_less_real: fun_re413263731l_bool ).
tff('#skF_19',type,
'#skF_19': ( nat * fun_nat_bool ) > nat ).
tff(power_power_nat,type,
power_power_nat: nat > fun_nat_nat ).
tff(m1,type,
m1: int ).
tff('#skF_1',type,
'#skF_1': ( fun_int_bool * int * int ) > int ).
tff('#skF_4',type,
'#skF_4': ( real * nat ) > real ).
tff(number_number_of_nat,type,
number_number_of_nat: int > nat ).
tff('#skF_8',type,
'#skF_8': fun_int_bool > nat ).
tff(tn,type,
tn: nat ).
tff('#skF_7',type,
'#skF_7': fun_int_bool > nat ).
tff('#skF_15',type,
'#skF_15': int > nat ).
tff(plus_plus_nat,type,
plus_plus_nat: nat > fun_nat_nat ).
tff('#skF_20',type,
'#skF_20': ( nat * nat * fun_nat_nat ) > nat ).
tff(hAPP_int_int,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(hAPP_i1948725293t_bool,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(hAPP_nat_bool,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff('#skF_6',type,
'#skF_6': fun_int_bool > int ).
tff('#skF_14',type,
'#skF_14': ( nat * fun_nat_bool ) > nat ).
tff(one_one_nat,type,
one_one_nat: nat ).
tff('#skF_11',type,
'#skF_11': int > nat ).
tff(plus_plus_int,type,
plus_plus_int: int > fun_int_int ).
tff('#skF_12',type,
'#skF_12': int > nat ).
tff(ord_less_eq_int,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(times_times_int,type,
times_times_int: ( int * int ) > int ).
tff(hAPP_nat_int,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(pls,type,
pls: int ).
tff(hAPP_nat_nat,type,
hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(zero_zero_nat,type,
zero_zero_nat: nat ).
tff(fFalse,type,
fFalse: bool ).
tff('#skF_2',type,
'#skF_2': int > nat ).
tff(hAPP_real_bool,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(ord_less_nat,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff('#skF_17',type,
'#skF_17': ( nat * nat * fun_nat_nat ) > nat ).
tff(bit0,type,
bit0: int > int ).
tff(hBOOL,type,
hBOOL: bool > $o ).
tff('#skF_10',type,
'#skF_10': ( int * int ) > nat ).
tff(power_power_int,type,
power_power_int: int > fun_nat_int ).
tff(sqrt,type,
sqrt: real > real ).
tff(hAPP_r1134773055l_bool,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(ord_less_eq_nat,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(t,type,
t: int ).
tff('#skF_3',type,
'#skF_3': ( nat * nat ) > nat ).
tff(zero_zero_int,type,
zero_zero_int: int ).
tff(f_590,axiom,
! [K: int] : ( number_number_of_int(K) = K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).
tff(f_357,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_semiring__norm_I112_J) ).
tff(f_1047,axiom,
! [M_4: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_4)),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_of__nat__less__0__iff) ).
tff(f_1282,axiom,
! [A_40: int] : ( hAPP_int_int(plus_plus_int(zero_zero_int),A_40) = A_40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__0__left) ).
tff(f_454,axiom,
! [W_3: int] : ( number_number_of_int(bit0(W_3)) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(W_3))),number_number_of_int(W_3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_number__of__Bit0) ).
tff(f_70,axiom,
hAPP_int_int(plus_plus_int(one_one_int),one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_semiring__one__add__one__is__two) ).
tff(f_144,axiom,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_nat__1__add__1) ).
tff(f_2296,axiom,
! [K_3: int] : ( number_number_of_int(succ(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_number__of__succ) ).
tff(f_2947,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_1038,axiom,
! [A_24: int,Na: nat] :
( ( hAPP_nat_int(power_power_int(A_24),Na) = zero_zero_int )
<=> ( ( A_24 = zero_zero_int )
& ( Na != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_power__eq__0__iff) ).
tff(f_2239,axiom,
! [K: int] : ( succ(K) = hAPP_int_int(plus_plus_int(K),one_one_int) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_succ__def) ).
tff(f_945,axiom,
! [A_59: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_59),hAPP_int_int(plus_plus_int(A_59),one_one_int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_less__add__one) ).
tff(c_511,plain,
! [K_196: int] : ( number_number_of_int(K_196) = K_196 ),
inference(cnfTransformation,[status(thm)],[f_590]) ).
tff(c_337,plain,
number_number_of_int(pls) = zero_zero_int,
inference(cnfTransformation,[status(thm)],[f_357]) ).
tff(c_2260,plain,
zero_zero_int = pls,
inference(demodulation,[status(thm),theory(equality)],[c_511,c_337]) ).
tff(c_844,plain,
! [M_4_398: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_4_398)),zero_zero_int)),
inference(cnfTransformation,[status(thm)],[f_1047]) ).
tff(c_2289,plain,
! [M_4_398: nat] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M_4_398)),pls)),
inference(demodulation,[status(thm),theory(equality)],[c_2260,c_844]) ).
tff(c_1078,plain,
! [A_40_555: int] : ( hAPP_int_int(plus_plus_int(zero_zero_int),A_40_555) = A_40_555 ),
inference(cnfTransformation,[status(thm)],[f_1282]) ).
tff(c_421,plain,
! [W_3_157: int] : ( hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(zero_zero_int),number_number_of_int(W_3_157))),number_number_of_int(W_3_157)) = number_number_of_int(bit0(W_3_157)) ),
inference(cnfTransformation,[status(thm)],[f_454]) ).
tff(c_2233,plain,
! [W_3_157: int] : ( hAPP_int_int(plus_plus_int(W_3_157),W_3_157) = bit0(W_3_157) ),
inference(demodulation,[status(thm),theory(equality)],[c_1078,c_511,c_511,c_511,c_421]) ).
tff(c_50,plain,
number_number_of_int(bit0(bit1(pls))) = hAPP_int_int(plus_plus_int(one_one_int),one_one_int),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_2458,plain,
bit0(bit1(pls)) = bit0(one_one_int),
inference(demodulation,[status(thm),theory(equality)],[c_2233,c_511,c_50]) ).
tff(c_118,plain,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(cnfTransformation,[status(thm)],[f_144]) ).
tff(c_2461,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(bit0(one_one_int)),
inference(demodulation,[status(thm),theory(equality)],[c_2458,c_118]) ).
tff(c_1656,plain,
! [K_3_1024: int] : ( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3_1024)) = number_number_of_int(succ(K_3_1024)) ),
inference(cnfTransformation,[status(thm)],[f_2296]) ).
tff(c_2190,plain,
! [K_3_1024: int] : ( hAPP_int_int(plus_plus_int(one_one_int),K_3_1024) = succ(K_3_1024) ),
inference(demodulation,[status(thm),theory(equality)],[c_511,c_511,c_1656]) ).
tff(c_2052,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(cnfTransformation,[status(thm)],[f_2947]) ).
tff(c_2215,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(demodulation,[status(thm),theory(equality)],[c_2190,c_2052]) ).
tff(c_2283,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_2260,c_2215]) ).
tff(c_2395,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_118,c_2283]) ).
tff(c_2469,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_2461,c_2395]) ).
tff(c_838,plain,
! [A_24_394: int,Na_395: nat] :
( ( zero_zero_int = A_24_394 )
| ( hAPP_nat_int(power_power_int(A_24_394),Na_395) != zero_zero_int ) ),
inference(cnfTransformation,[status(thm)],[f_1038]) ).
tff(c_3409,plain,
! [A_24_2025: int,Na_2026: nat] :
( ( pls = A_24_2025 )
| ( hAPP_nat_int(power_power_int(A_24_2025),Na_2026) != pls ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2260,c_2260,c_838]) ).
tff(c_3423,plain,
succ(hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(superposition,[status(thm),theory(equality)],[c_2469,c_3409]) ).
tff(c_1636,plain,
! [K_1006: int] : ( hAPP_int_int(plus_plus_int(K_1006),one_one_int) = succ(K_1006) ),
inference(cnfTransformation,[status(thm)],[f_2239]) ).
tff(c_781,plain,
! [A_59_353: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_59_353),hAPP_int_int(plus_plus_int(A_59_353),one_one_int))),
inference(cnfTransformation,[status(thm)],[f_945]) ).
tff(c_2172,plain,
! [A_59_353: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,A_59_353),succ(A_59_353))),
inference(demodulation,[status(thm),theory(equality)],[c_1636,c_781]) ).
tff(c_3428,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,n)),pls)),
inference(superposition,[status(thm),theory(equality)],[c_3423,c_2172]) ).
tff(c_4531,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2289,c_3428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM925_2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:03:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 14.93/4.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.93/4.73
% 14.93/4.73 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.93/4.76
% 14.93/4.76 Inference rules
% 14.93/4.76 ----------------------
% 14.93/4.76 #Ref : 6
% 14.93/4.76 #Sup : 502
% 14.93/4.76 #Fact : 1
% 14.93/4.76 #Define : 0
% 14.93/4.76 #Split : 2
% 14.93/4.76 #Chain : 0
% 14.93/4.76 #Close : 0
% 14.93/4.76
% 14.93/4.76 Ordering : KBO
% 14.93/4.76
% 14.93/4.76 Simplification rules
% 14.93/4.76 ----------------------
% 14.93/4.76 #Subsume : 327
% 14.93/4.76 #Demod : 808
% 14.93/4.76 #Tautology : 584
% 14.93/4.76 #SimpNegUnit : 61
% 14.93/4.76 #BackRed : 5
% 14.93/4.76
% 14.93/4.76 #Partial instantiations: 155
% 14.93/4.76 #Strategies tried : 1
% 14.93/4.76
% 14.93/4.76 Timing (in seconds)
% 14.93/4.76 ----------------------
% 14.93/4.76 Preprocessing : 1.71
% 14.93/4.76 Parsing : 0.91
% 14.93/4.76 CNF conversion : 0.14
% 14.93/4.76 Main loop : 1.99
% 14.93/4.76 Inferencing : 0.22
% 14.93/4.76 Reduction : 1.09
% 14.93/4.76 Demodulation : 0.82
% 14.93/4.76 BG Simplification : 0.15
% 14.93/4.76 Subsumption : 0.42
% 14.93/4.76 Abstraction : 0.05
% 14.93/4.76 MUC search : 0.00
% 14.93/4.76 Cooper : 0.00
% 14.93/4.76 Total : 3.75
% 14.93/4.76 Index Insertion : 0.00
% 14.93/4.77 Index Deletion : 0.00
% 14.93/4.77 Index Matching : 0.00
% 14.93/4.77 BG Taut test : 0.00
%------------------------------------------------------------------------------